# Step 1: Install and load the deSolve package
library(deSolve)

# Step 2: Prepare your data in R or import it from a CSV file
data <- data.frame(
  time = c(0, 1, 2, 3, 4),
  variable = c(1, 2, 3, 4, 5)
)

# Step 3: Define your model function, which includes the time-varying variable
model <- function(t, y, parameters, data) {
  k <- parameters["k"]
  variable_data <- approxfun(data$time, data$variable)(t)
  
  dydt <- -k * y + variable_data
  list(dydt)
}

# Step 4: Set up the initial conditions, time points, and parameters
y0 <- 0
t <- seq(0, max(data$time), length.out = 100)
parameters <- list(k = 0.1)  # Decay constant (you can adjust this value)

# Step 5: Solve the ODE using ode function from deSolve
solution <- ode(y = y0, times = t, func = model, parms = parameters, data = data)

# Step 6: Plot the results
plot(data$time, data$variable, type = "b", pch = 16, col = "blue", xlab = "Time", ylab = "Variable", main = "Dissolve Model")
lines(solution, col = "red", lwd = 2)
legend("topleft", legend = c("Data", "Model"), col = c("blue", "red"), lwd = 2, pch = 16)